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Problem Statement:
A nutritionist wants to explore the relationship between muscle mass
(\(Y\)) and age (\(X\)) in women. The goal is to fit a
first-order regression model and analyze the relationship.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 156.346564 | 5.5122625 | 28.36341 | 0 |
| X | -1.189995 | 0.0901973 | -13.19326 | 0 |
Problem Statement:
Extend the analysis by fitting a second-order (quadratic) regression
model and evaluating its fit. Additionally, predict the mean and
individual muscle mass for a 48-year-old woman.
| Estimate | Std. Error | t value | Pr(>|t|) | |
|---|---|---|---|---|
| (Intercept) | 82.9357488 | 1.5431459 | 53.744593 | 0.0000000 |
| x_centered | -1.1839580 | 0.0886330 | -13.357984 | 0.0000000 |
| I(x_centered^2) | 0.0148405 | 0.0083566 | 1.775902 | 0.0810869 |
| Type | Lower | Upper |
|---|---|---|
| Confidence Interval | 96.28436 | 102.2249 |
| Prediction Interval | 82.91160 | 115.5976 |